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In this paper, we model and analyze the end-to-end energy consumption of 100-Gbps coherent long-haul transmission systems. In particular, we investigate the impact of forward error correction (FEC) on the end-to-end energy consumption. We compare the energy efficiency of commonly used modulation formats in 100-Gbps transmission, namely dual polarization-quadrature phase-shift-keying (DP-QPSK) and dual polarization-16-quadrature amplitude modulation (DP-16-QAM), for different transmission distance and input bit error rate. Our energy model includes consumption of transmitter, booster, link amplifier as well as receiver. Compared with previous digital signal processing models, we provide a very detailed model that not only includes all the significant functional blocks (such as timing and carrier recovery, chromatic and polarization mode dispersion compensation, and FEC), but also takes into account impact of the number of samples processed every clock cycle and of operations other than multiplications. We have found that receiver energy consumption dominates in transmission systems that use electronic dispersion compensation over long transmission distances. Our results show that for short transmission distances where hard-decision decoding is adequate for both modulation formats, DP-16-QAM is more energy efficient than DP-QPSK. However, as the transmission distance increases, the energy saving due to the low symbol rate of DP-16-QAM is offset by the energy consumption of soft-decision decoding. In this case, the two modulation formats have approximately similar energy consumption.